0.021699
3
2,1,2
1.039682
0.006
0.004911
3
2,2,1
1.039682
0.0255
0.020871
3
2,2,2
1.092727
0.1445
0.107068
The incomes
y
t
(
λ
t
), probabilities
π
t
(
λ
t
), and contingent claims prices
q
t
(
λ
t
) are
computed using the above formulae.
The price of a riskless bond at time
t
is simply the sum of all contingent claims
prices to consumption at
t
.
See the column of the table labeled BOND.
For comparison,
note that
β
= 0.96,
β
2
= 0.9216, and
β
3
= 0.884736, so the rate of return on a bond is less
than the discount rate.
d)
The price of a bond at time
t
contingent on
λ
t
=
λ
1
is obtained by summing over
the prices of contingent claims for histories where
λ
t
=
λ
1
.
See the column of the table
labeled BOND 1.
e)
The price of a bond at time
t
contingent on
λ
t
=
λ
2
is obtained by summing over
the prices of contingent claims for histories where
λ
t
=
λ
2
.
See the column of the table
labeled BOND 2.
f)
Clearly the price of a riskless bond is the sum of the price of a bond that pays off
if
λ
t
=
λ
1
and the price of a bond that pays off if
λ
t
=
λ
2
since these are the only two
possibilities.
2)
An economy consists of two infinitely-lived consumers named
i
= 1, 2.
There is
one nonstorable consumption good.
Consumer i consumes
c
i
t
at time
t
and ranks
consumption streams by
∑
∞
=
0
)
(
t
t
i
t
c
u
β
,
where
β
∈
(0, 1) and
u
(
c
) is increasing, strictly concave, and
C
2
.
Consumer 1 is endowed
with a stream of consumption
y
1
t
= (1, 0, 0, 1, 0, 0, 1, . . . ).
Consumer 2 is endowed with
a stream of consumption
y
2
t
= (0, 1, 1, 0, 1, 1, 0, . . . ).
Assume there are complete
markets with time 0 trading.